Download Geometry

Name: ______________________
Geometry A U4D5 Midsegments
Warm Up Name a Pair of:
•
VERTICAL ANGLES
•
CORRESPONDING ANGLES
•
ALTERNATE INTERIOR ANGLES
•
ALTERNATE EXTERIOR ANGLES
•
SUPPLEMENTARY ANGLES
1) Solve for x.
2) Solve for x.
Date: ______________
Investigate the mid-segments of a triangle
Plot the following points to create a triangle: A(0, 2); B(- 8, 2) and C (-8, 8)
1. Find the midpoints of all 3 sides of the triangle. Label them D, E and F.
2. Connect these 3 midpoints to form the 3 mid-segments.
3. Find all the side lengths of the triangle:
AB=_____ BC=____ AC=____
4. Find the mid-segment lengths and label them. DE=____ EF=____ DF=___
What do you notice about the lengths of the mid-segments compared to the opposite sides of
the triangle?
5. Find the slope of all 3 mid-segments:
slope AB=________ slope BC=________ slope AC=________
slope DE=________ slope EF=________ slope DF=________
What do you notice about the slopes of the mid-segments compared to the slopes of the
opposite sides of the triangle? What can you conclude?
Name: ______________________
Date: ______________
Geometry A U4D5 Midsegments Notes
Example 1: Another way of exploring midsegments. The accompanying
diagram shows a section of the city of Tacoma. High Road, State Street, &
Main Street are parallel and 5 miles apart. Ridge Road is perpendicular to
the three parallel streets. The distance between the intersection of Ridge
Road and State Street and where the railroad tracks cross State Street is
12 miles.
a. Find the distance from the intersection of Ridge Road and Main
Street to Main Street’s intersection with the railroad tracks.
b. Find the length of railroad tracks from Ridge Road to Main Street.
c. What 3 facts indicate that State Street acts as the midsegment of the triangle formed?
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
Example 2: Mr. Paley is setting up a swing set for his
children. For stability, he buried the legs of the A-frame in
concrete. The cross bars will support the structure at the
halfway point in the angle. The cross bars are 36 inches
long. How far apart are the bottom of the A frames?
Example 3:
1) In triangle XYZ, M, N, and P are midpoints. The perimeter of triangle MNP is 60.
Find NP
Find YZ
Example 4: N and M are midpoints of AC and AB in triangle ABC.
Use parallel lines cut by a transversal!!!
Find ∠𝐴𝑀𝑁
Find ∠𝐴𝑁𝑀
Find ∠𝐴
5) Blast from the Past: The widths of two similar prisms are 8 cm and 18 cm.
What is the ratio of the perimeters?
Of the areas?
of the Volumes?
6)
a)
b) Give two explanations of why DE can NOT be a midsegment.
____________________________________________________________________________
____________________________________________________________________________
Name: ______________________
Date: ______________
Geometry A U4D5 Midsegments HW
1) If 2 similar trapezoids have a scale factor of 3:2 for their corresponding sides, then
a) the ratio of the corresponding perimeters is________.
b) the ratio of the corresponding areas is________.
2) If the ratio of corresponding heights of 2 similar cones is 5:3, then what is the ratio of their
volumes?
3) Find DE.
4) T is the midpoint of
. U is the midpoint of
a. Find m∠QSR.
5)
What theorem are you using?
6)
. m∠QUT = 85 and RS = 36.
b. Find TU.
Illustrating the mid-segment theorem:
Graph: J(-2, 3) K(4, 5) L(6, -1)
Show that the mid-segment MN is parallel to the side JK and half its
length.
7) Find the midpoints:
M=
N=
8) Find the slopes:
MN=
JK =
9) Find the lengths:
MN=
JK=
10) The base of the Transamerica Building in San
Francisco, CA, is 145 feet. If the distance from a base
corner of the building to its peak is 856 feet, how wide is it
halfway to the top?
Name: ______________________
Date: ______________
Geometry A U4D5 Midsegments GROUP QUIZ
1) Find LM explain why
2) Find the value of x.
3) DE is a mid-segment of triangle CAB.
Find the measure of angle CED.
Find the measure of angle BED.
4) Given AC = 6, CB =5, AB = 9. A, B & C are midpoints.
Find the perimeter of ΔPQR.
5) In triangle GHI, R, S, and T are midpoints. Show work by labeling diagrams.
A. If GH = 20 and HI = 18, find RT.
B. If RH = 7 and RS = 5, find ST.
C. If m  G = 60 and m  I = 70, find m  GTR.
D. If m  H = 50 and m  I = 66, find m  ITS.
E. If m  G = m  H = m  I and RT = 15, find the perimeter of
 GHI.